Plane on a conveyor belt

DiscoStu

Sambostar said:

But at the end of the day, the wheels are going faster than the treadmill, which the question states cannot happen.  Despite whatever forces are at play.  So yeah, it'll take off, but you haven't read the question.

This example does not represent the conditions set out in the original question so does not apply to the scenario we are arguing about.

As the speed of the treadmill increases in the vid he increases the power of the plane to match it and the plane stays stationary, but he 'solves' the puzzle by keeping the treadmill at 9mph and then increasing the power of the plane so that the wheels can turn faster than 9mph and it moves forward.
The puzzle states that the treadmill's speed always matches the rotation speed of the wheels and when this scenario was being fulfulled in the video - no matter if the plane's wheels were turning at 1mph or 9mph - the plane did not move. No movement = no airflow over wings = no lift.

The unconventional properties required of the conveyor belt would effectively make it a freewheel so perhaps if we swap it for a rolling road or giant freewheels underneath each of the plane's wheels it may make more sense. A freewheel sitting on top another freewheel doesn't go anywhere when turned and you need the upper wheel to outrun the bottom one for the plane to move forward and take off but it cannot do that.

Emp_Fab

CabbageCat said:

Emp_Fab said:

Well, I'm happy with my understanding of it.  It all works with Newton's laws, it's absolutely not a paradox.  Thinking it is is just a get-out from working out what's actually going on.  Nothing runs at the speed of infinity and it can be implemented in reality without the universe collapsing to a singularity.

"I don't like that question so I'll answer one that I do like."

We have to either break the laws of physics, the plane, the conveyor or the question. 

Not at all.  I've answered not only the question posed, but also the other wording of it.  If you can't understand the physics, then that's not really anything to do with me.  It's more a case of "I don't understand your answer, so I'll accuse you of not answering the question".

DiscoStu

This video shows you the environment as set out in the original question posed.
As more power is applied, the wheels turn faster but as the surface on which the bike is sitting instantly matches the wheel's rotation but in an opposite direction the bike remains stationary, even when she is freewheeling and applying no direct drive to the rear wheel the bike still does not move as the surface it is on cancels out forward motion.

viz

^ That's not the same as the OP question. The way that is set up, there is no forward thrust being created; the force is fully converted to angular momentum, and probably drives the clutch on the conveyor too. Also as Axe_meister is probably going to point out shortly, the cyclist is driving the wheels, whereas in the OP, the wheels are not driven. The equivalent would be if you tried to pull the bike forward off the apparatus, how fast would the wheels have to turn to prevent you? And the answer is, not even infinitely fast would be enough, because the apparatus doesn't provide any opposing force to forward motion.  

Axe_meister

DiscoStu said:

This video shows you the environment as set out in the original question posed.
As more power is applied, the wheels turn faster but as the surface on which the bike is sitting instantly matches the wheel's rotation but in an opposite direction the bike remains stationary, even when she is freewheeling and applying no direct drive to the rear wheel the bike still does not move as the surface it is on cancels out forward motion.

No it does not because in the video the wheels are driven. In the aircraft example the wheels are just free wheeling.
To stop the aircraft from moving you would have to apply a force to the wheels equal to the thrust of the aircraft, but as the wheels are free to move you will just increase the speed of the wheels.

DiscoStu

Does anyone have a set of bike rollers? We can solve this once and for all if someone does.
Get bike up to speed then stop pedalling to enter freewheel mode. Ask someone to nudge you from behind and see what happens. Do you move forward off the rollers or does the bike stay where it is but with higher wheel/roller speed?

And then we can go to the pub.

viz

Exactly! And the answer is, you'd move forwards. Also by the way, if you applied the brakes sharply you'd stay in position and all the wheels would come to a stop, but if someone pushed you from the front you'd move backwards. 

HAL9000

Drew_TNBD said:

I've got an even better paradox...

Which brand of mermaid would you bone?


https://dl.dropboxusercontent.com/u/630473/mermaids.png

Not tonight darling, I've got a bit of a haddock. 

CabbageCat

Emp_Fab said:

CabbageCat said:

Emp_Fab said:

Well, I'm happy with my understanding of it.  It all works with Newton's laws, it's absolutely not a paradox.  Thinking it is is just a get-out from working out what's actually going on.  Nothing runs at the speed of infinity and it can be implemented in reality without the universe collapsing to a singularity.

"I don't like that question so I'll answer one that I do like."

We have to either break the laws of physics, the plane, the conveyor or the question. 

Not at all.  I've answered not only the question posed, but also the other wording of it.  If you can't understand the physics, then that's not really anything to do with me.  It's more a case of "I don't understand your answer, so I'll accuse you of not answering the question".

So, in your situation at no stage are the planes wheels turning faster than the conveyor?

Danny1969

I'm probably wrong but I think the jet engine would propel the plane forward and all the conveyor belt would do is spin the wheels of the plane but that wouldn't do anything cos they aren't connected to anything ..... as I said I'm wrong it can't be that simple can it ?

viz

Danny1969 said:

I'm probably wrong but I think the jet engine would propel the plane forward and all the conveyor belt would do is spin the wheels of the plane but that wouldn't do anything cos they aren't connected to anything ..... as I said I'm wrong it can't be that simple can it ?

You're right, the only thing to add is that the conveyor belt would try to spin to infinity (or at least it would spin the aeroplane's wheels up to their maximum speed, at which point they'd catch fire) - and the plane would scrape forward and take off. 

DiscoStu

DiscoStu said:

Does anyone have a set of bike rollers? We can solve this once and for all if someone does.
Get bike up to speed then stop pedalling to enter freewheel mode. Ask someone to nudge you from behind and see what happens. Do you move forward off the rollers or does the bike stay where it is but with higher wheel/roller speed?

And then we can go to the pub.

viz said:

Exactly! And the answer is, you'd move forwards. Also by the way, if you applied the brakes sharply you'd stay in position and all the wheels would come to a stop, but if someone pushed you from the front you'd move backwards. 

My feeling is that the external force applied would push the bike forwards momentarily but in doing so would have to increase the wheel speed...which would increase the roller speed and we're back where we started.

Given that a conveyor belt has a continual surface I see it that each increase in force would make the bike/plane stutter forwards slightly but the conveyor would almost instantly catch up with the increasing wheel speed and it would return to a stationary position as was shown in the model plane/treadmill vid. He didn't always have the plane and treadmill matched so the plane went forwards and backwards but as soon as they equalled out the plane became stationary again.

I don't think the 747's wheels could possibly outrun the belt/rollers by over 150mph (to achieve lift off) because that's what would have to happen. The motion created by the force of the engines would have to result in the wheels turning faster if it is to move forwards and the belt cancels it out. I think there would be a series of forward judders followed by stationary position.

viz

DiscoStu said:

Given that a conveyor belt has a continual surface I see it that each increase in force would make the bike/plane stutter forwards slightly but the conveyor would almost instantly catch up with the increasing wheel speed and it would return to a stationary position as was shown in the model plane/treadmill vid. He didn't always have the plane and treadmill matched so the plane went forwards and backwards but as soon as they equalled out the plane became stationary again.

Yep, and that's because the plane's wheels create drag on the plane. If they were really free-wheeling, the conveyor would have to be infinitely fast. So, depends on whether it's a pure maths problem or an engineering problem. If engineering, then you'd reach equilibrium between the forward thrust of the propellor and the resistance of the wheels, and the treadmill keeping up. As soon as you exceed the thrust forwards, the conveyor needs to speed up, and if you keep that force constant, the conveyor needs to reach infinity and still can't stop it. 

JohnnyPlectrum

DiscoStu said:

I don't think the 747's wheels could possibly outrun the belt/rollers by over 150mph (to achieve lift off) because that's what would have to happen. The motion created by the force of the engines would have to result in the wheels turning faster if it is to move forwards and the belt cancels it out. I think there would be a series of forward judders followed by stationary position.

I think there would be one instantaneous ramp up to oblivion the moment the plane's thrust was applied. Once 'stiction' is beaten there's nowt to resist the thrust and the treadmill would just spin up in an attempt to.

Maybe it could be crowd-funded?

HAL9000

viz said:

The equivalent would be if you tried to pull the bike forward off the apparatus, how fast would the wheels have to turn to prevent you? And the answer is, not even infinitely fast would be enough, because the apparatus doesn't provide any opposing force to forward motion.  

It doesn't need to. The rule about instantly and exactly matching the belt's speed to that of the wheels is sufficient.

A5D5E5

DiscoStu said:

This video shows you the environment as set out in the original question posed.
As more power is applied, the wheels turn faster but as the surface on which the bike is sitting instantly matches the wheel's rotation but in an opposite direction the bike remains stationary, even when she is freewheeling and applying no direct drive to the rear wheel the bike still does not move as the surface it is on cancels out forward motion.

If somebody tied a rope to the bike and pulled it forwards then you would have an analogy for a real plane on a real conveyor, though not necessarily for the original question because of the constraints it contains about wheel speed and conveyor speed.

viz

HAL9000 said:

viz said:

The equivalent would be if you tried to pull the bike forward off the apparatus, how fast would the wheels have to turn to prevent you? And the answer is, not even infinitely fast would be enough, because the apparatus doesn't provide any opposing force to forward motion.  

It doesn't need to. The rule about instantly and exactly matching the belt's speed to that of the wheels is sufficient.

True but in the pure maths experiment you reach infinite speed instantly, and then you're in the realm of "can the bike wheels' infinite speed be faster than the conveyor's wheels' infinite speed?" issue. 

Handsome_Chris

I'm surprised that none of you self-proclaimed brainiacs out there have not point this out, but it is impossible for the conveyor belt to have the same rotational speed as the wheels.

If the runaway is 3.902 km. Then the belt of the conveyor belt is going to have to be at least twice that.  Let's call it a round 8000 metres once we've added the rollers at the end and allowed for a drive mechanism to move this beast. 

The next thing to consider is that the diameter of the wheels is 46 inches, which works out as a circumference of 144.513262065 inches or approximately 3.671 metres. 

The bottom line is that the wheel will do approximately 2179.2427 rotations to every one rotation of the conveyor belt.  

You can't argue with maths

Ravenous

Handsome_Chris said:

The bottom line is that the wheel will do approximately 2179.2427 rotations to every one rotation of the conveyor belt.  

Hey guys, I think we've found a drummer!

DiscoStu

If the rollers driving the conveyor belt are the same size as the wheels on the plane then their rotation speeds would be identical. If the wheels are all 1 metre diameter then one rotation = 3.14m of belt travel, the circumference of all the wheels.